Single point incremental forming process (SPIF) has a great potential to manufacture customized products with complex shapes using a simple tool. Recently, this technology has been employed in several applications, especially in aircraft and biomedical industries. During SPIF process, the sheet metal is clamped by a blank-holder and a hemispherical tool moves along a specified path to deform the sheet incrementally. Usually, the forming operation is performed by conventional CNC machine tools. In recent years, industrial robots have also been tested to reduce tooling manufacturing costs and improve production versatility. For these machines, the prediction of forming forces associated to an elastic modeling of the robot is necessary to compensate tool path errors due to the robot compliance and to ensure the geometrical quality of the final part. The forming forces are usually predicted from a Finite Element (FE) analysis of the process and are used as input data for the elastic modeling of the robot to predict the tool path deviation [1]. However, the reliability of the predicted loads depends strongly on the mechanical model of the blank considered in the simulation of the SPIF process. In the last decade, as long as SPIF process is concerned, only few works have investigated the effect of mechanical models on the forces predicted by FE analysis. Henrard et al. [2] and Flores et al. [3] have compared the influence of different plastic behaviors (plastic criterion, hardening law, strain hardening type) on the force prediction for AA3003-O. Results show that forming forces depend more on the hardening law than on the yield locus. If contradictory conclusions are presented on the need to consider an isotropic or a mixed strain hardening, the hardening law is presented as one of the most influent modeling parameter on the force level. As shown by the previous studies, selecting the suitable material model to predict accurate forming forces is still a challenging task. These difficulties mainly lie in high plastic strain levels (larger than 100%) and complex strain paths observed in this process [3]. In this context, the final aim of this study is to investigate the impact of constitutive models of titanium T40 blank on the SPIF forming load predictions.

As a first step, in this paper, experimental results of uniaxial tensile tests and simple shear tests, both performed at several orientations from the rolling direction, as well as reversed shear tests are firstly presented. From this database, material parameters of classical anisotropic elasto-plastic model are identified. Secondly, the forming of a truncated cone made from a T40 alloy is carried out with a three-axis CNC milling machine. FE analysis is then performed using the above calibrated mechanical model, and the thickness variation, the final geometry and the load are predicted and compared with experimental data.

[1] Belchior, J., (2013). Développement d'une approche couplée matériau/structure machine: application au formage incrémental robotisé. Doctoral dissertation, INSA de Rennes.

[2] Henrard, C., Bouffioux, C., Eyckens, P., Sol, H., Duflou, J. R., Van Houtte, P., Van Bael, A., Duchêne, L. and Habraken, A. M. (2011). Forming forces in single point incremental forming: prediction by finite element simulations, validation and sensitivity. Computational mechanics, 47(5), 573-590.

[3] Flores, P., Duchene, L., Bouffioux, C., Lelotte, T., Henrard, C., Pernin, N., Van Bael, A., He, S., Duflou, J. and Habraken, A. M. (2007). Model identification and FE simulations: effect of different yield loci and hardening laws in sheet forming. International journal of plasticity, 23(3), 420-449.